English
Related papers

Related papers: Symplectic duality and implosions

200 papers

We review the quiver descriptions of symplectic and hyperk\"ahler implosion in the case of SU(n) actions. We give quiver descriptions of symplectic implosion for other classical groups, and discuss some of the issues involved in obtaining a…

Symplectic Geometry · Mathematics 2014-12-02 Andrew Dancer , Brent Doran , Frances Kirwan , Andrew Swann

We use Nahm data to give a description of a candidate for the universal hyperkahler implosion with respect to a compact Lie group

Symplectic Geometry · Mathematics 2016-01-20 Andrew Dancer , Frances Kirwan , Markus Roeser

We give a survey of the implosion construction, extending some of its aspects relating to hypertoric geometry from type $A$ to a general reductive group, and interpret it in the context of the Moore-Tachikawa category. We use these ideas to…

Symplectic Geometry · Mathematics 2024-08-22 Andrew Dancer , Frances Kirwan , Johan Martens

The purpose of this paper is twofold. First we extend the notion of symplectic implosion to the category of quasi-Hamiltonian $K$-manifolds, where $K$ is a simply connected compact Lie group. The imploded cross-section of the double…

Symplectic Geometry · Mathematics 2007-05-23 Jacques Hurtubise , Lisa Jeffrey , Reyer Sjamaar

We review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of $x-y$ dualities in a broader context of log…

Mathematical Physics · Physics 2024-12-05 Alexander Alexandrov , Boris Bychkov , Petr Dunin-Barkowski , Maxim Kazarian , Sergey Shadrin

Let $K$ be a compact Lie group. We introduce the process of symplectic implosion, which associates to every Hamiltonian $K$-manifold a stratified space called the imploded cross-section. It bears a resemblance to symplectic reduction, but…

Symplectic Geometry · Mathematics 2007-05-23 Victor Guillemin , Lisa Jeffrey , Reyer Sjamaar

The geometry of the universal hyperKaehler implosion for SU(n) is explored. In particular, we show that the universal hyperKaehler implosion naturally contains a hypertoric variety described in terms of quivers. Furthermore, we discuss a…

Symplectic Geometry · Mathematics 2014-02-12 Andrew Dancer , Frances Kirwan , Andrew Swann

We propose quivers for Coulomb branch constructions of universal implosions for orthogonal and symplectic groups, extending the work on special unitary groups in arXiv:2004.09620. The quivers are unitary-orthosymplectic as opposed to the…

High Energy Physics - Theory · Physics 2021-08-18 Antoine Bourget , Andrew Dancer , Julius F. Grimminger , Amihay Hanany , Frances Kirwan , Zhenghao Zhong

For any k<2n we construct a complete system of invariants in the problem of classifying singularities of immersed k-dimensional submanifolds of a symplectic 2n-manifold at a generic double point.

Symplectic Geometry · Mathematics 2016-10-03 W. Domitrz , S. Janeczko , M. Zhitomirskii

This is a survey written in an expositional style on the topic of symplectic singularities and symplectic resolutions, which could also serve as an introduction to this subject.

Algebraic Geometry · Mathematics 2007-05-23 Baohua Fu

We study the holomorphic symplectic structures on hyper-Kaehler manifolds of type A_{\infty}, by using the torus action.

Differential Geometry · Mathematics 2013-01-22 Kota Hattori

We derive a symplectic analogue of A-directed immersion theorem.

Symplectic Geometry · Mathematics 2015-07-21 Sauvik Mukherjee

We completely characterize cosymplectic and $\alpha$-cosymplectic Lie algebras in terms of corresponding symplectic Lie algebras and suitable derivations on them. Several examples are given and classification results are obtained in…

Differential Geometry · Mathematics 2016-01-19 Giovanni Calvaruso , Antonella Perrone

This paper is devoted to the study of symplectic manifolds and their connection with Hamiltonian dynamical systems. We review some properties and operations on these manifolds and see how they intervene when studying the complete…

Symplectic Geometry · Mathematics 2019-04-03 A. Lesfari

In this short note, we make an observation relating symplectic packings of the standard symplectic ball by two sets and Hamiltonian linking.

Symplectic Geometry · Mathematics 2025-07-03 Dylan Cant

We state a conjecture about the volume of symplectically self-polar convex bodies and show that it is equivalent to Mahler's conjecture concerning the volume of a convex body and its Euclidean polar. We also establish lower and upper bounds…

Metric Geometry · Mathematics 2025-12-02 Mark Berezovik , Roman Karasev

We study the local symplectic algebra of the 1-dimensional isolated complete intersection singularity of type S{\mu}. We use the method of algebraic restrictions to classify symplectic S{\mu} singularities. We distinguish these symplectic…

Symplectic Geometry · Mathematics 2012-11-07 Wojciech Domitrz , Żaneta Trȩbska

We develop a structure theory for nilpotent symplectic alternating algebras. We then give a classification of all nilpotent symplectic alternating algebras of dimension up to 10 over any field. The study reveals a new subclasses of powerful…

Rings and Algebras · Mathematics 2024-07-08 Layla Hamad Elnil Mugbil Sorkatti

We discuss some examples in which symplectic monodromy (provably or conjecturally) splits off the symplectic mapping class group, hoping to illustrate different techniques and inputs to the arguments. Along the way we formulate several open…

Symplectic Geometry · Mathematics 2026-01-29 Ailsa Keating , Ivan Smith , Michael Wemyss

We introduce a multiplicative version of complex-symplectic implosion in the case of $SL(n, \C)$. The universal multiplicative implosion for $SL(n, \C)$ is an affine variety and can be viewed as a nonreductive geometric invariant theory…

Symplectic Geometry · Mathematics 2015-08-17 Andrew Dancer , Frances Kirwan
‹ Prev 1 2 3 10 Next ›